This document provides diagnostic plots for several spawner-recruit models that were used to characterize Canadian-origin Yukon Chinook salmon population dynamics at the Conservation Unit scale as described in:

Connors, B.M., O’Dell, A., Hunter, H., Glaser, D., Gill, J., Rossi, S., and Churchland, C. In review. Stock status and biological and fishery consequences of alternative harvest and rebuilding actions for Yukon River Chinook salmon (Oncorhynchus tshawytscha). DFO Can. Sci. Advis. Sec. Res. Doc. 2025/nnn. iv + 92 p.

Full details are provided in the document above but briefly, four state-space spawner-recruit models were fit: spawer-recruitment models with autoregressive (AR1) recruitment residuals, (2) spawner-recruitment models with time varying intrinsic productivity, (3) egg mass-recruitment models with AR1 recruitment residuals, and (4) egg mass-recruitment models with time varying intrinsic productivity. The models

These models were fit to each of the nine Conservation Units for which we had data.

Diagnostics

We fit the spawner-recruitment model in a Bayesian estimation framework with Stan (Carpenter et al. 2017; Stan Development Team 2023), which implements the No-U-Turn Hamiltonian Markov chain Monte Carlo algorithm (Hoffman and Gelman 2014)) for Bayesian statistical inference to generate a joint posterior probability distribution of all unknowns in the model. The models can be found here.We sampled from 4 chains with 4,000 iterations each and discarded the first half as warm-up. We assessed chain convergence visually via trace plots and by ensuring that \(\hat{R}\) (potential scale reduction factor; Vehtari et al. 2021) was less than 1.01 and that the effective sample size was greater than 400. Posterior predictive checks were used to make sure the model returned known values, by simulating new datasets and checking how similar they were to our observed data.

Trace plots

These should be clearly mixed, with no single distribution deviating substantially from others (left column), and no chains exploring a strange space for a few iterations (right column).

Big.Salmon

MiddleYukonR.andtribs.

Nordenskiold

NorthernYukonR.andtribs.

Pelly

Stewart

UpperYukonR.

Whiteandtribs.

YukonR.Teslinheadwaters

ESS and \(\hat{R}\)

We aimed for minimum effective sample sizes that are greater than 2000 and \(\hat{R}\) values less than 1.05.

For the AR1 model:

CU ESS Rhat
Big.Salmon 379 1.025
MiddleYukonR.andtribs. 629 1.011
Nordenskiold 1329 1.006
NorthernYukonR.andtribs. 585 1.005
Pelly 295 1.016
Stewart 581 1.003
UpperYukonR. 636 1.009
Whiteandtribs. 474 1.007
YukonR.Teslinheadwaters 22 1.254

the time varying model:

CU ESS Rhat
Big.Salmon 390 1.014
MiddleYukonR.andtribs. 540 1.010
Nordenskiold 769 1.005
NorthernYukonR.andtribs. 321 1.006
Pelly 367 1.010
Stewart 525 1.014
UpperYukonR. 614 1.004
Whiteandtribs. 273 1.010
YukonR.Teslinheadwaters 491 1.018

the egg mass AR1 model:

CU ESS Rhat
Big.Salmon 132 1.031
MiddleYukonR.andtribs. 279 1.015
Nordenskiold 634 1.010
NorthernYukonR.andtribs. 170 1.017
Pelly 177 1.006
Stewart 324 1.014
UpperYukonR. 250 1.024
Whiteandtribs. 178 1.015
YukonR.Teslinheadwaters 254 1.034

and the time varying egg mass AR1 model:

CU ESS Rhat
Big.Salmon 118 1.035
MiddleYukonR.andtribs. 344 1.004
Nordenskiold 269 1.008
NorthernYukonR.andtribs. 181 1.015
Pelly 147 1.031
Stewart 335 1.019
UpperYukonR. 238 1.012
Whiteandtribs. 237 1.010
YukonR.Teslinheadwaters 277 1.027